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Some New Variance Bounds for Asset Prices

  • Charles Engel

When equity prices are determined as the discounted sum of current and expected future dividends, Shiller (1981) and LeRoy and Porter (1981) derived a relationship between the variance of the price of equities, p(t), and the variance of the ex post realized discounted sum of current and future dividends: p*(t): Var(p*(t))>= Var(p(t)). The literature has long since recognized that this variance bound is valid only when dividends follow a stationary process. Others, notably West (1988), derive variance bounds that apply when dividends are nonstationary. West shows that the variance in innovations in p(t) must be less than the variance of innovations in a forecast of the discounted sum of current and future dividends constructed by the econometrician, p^(t). Here we derive a new variance bound when dividends are stationary or have a unit root, that sheds light on the discussion in the 1980s of the Shiller variance bound: Var(p(t)-p(t-1)) >= Var(p*(t)-p*(t-1))! We also derive a variance bound related to the West bound: Var(p^(t)-p^(t-1)) >= Var(p(t)-p(t-1)).

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 10981.

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Date of creation: Dec 2004
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Publication status: published as Engel, Charles, 2005. "Some New Variance Bounds for Asset Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(5), pages 949-55, October.
Handle: RePEc:nbr:nberwo:10981
Note: AP
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  1. Kleidon, Allan W, 1986. "Variance Bounds Tests and Stock Price Valuation Models," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 953-1001, October.
  2. Kleidon, Allan W, 1988. "The Probability of Gross Violations of a Present Value Variance Inequality: Reply," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 1093-96, October.
  3. Shiller, Robert J, 1988. "The Probability of Gross Violations of a Present Value Variance Inequality," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 1089-92, October.
  4. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-74, May.
  5. Frankel, Jeffrey A. & Stock, James H., 1987. "Regression vs. volatility tests of the efficiency of foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 6(1), pages 49-56, March.
  6. Charles Engel & Kenneth D. West, 2003. "Exchange rates and fundamentals," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  7. Marsh, Terry A & Merton, Robert C, 1986. "Dividend Variability and Variance Bounds Tests for the Rationality ofStock Market Prices," American Economic Review, American Economic Association, vol. 76(3), pages 483-98, June.
  8. Mankiw, N Gregory & Romer, David & Shapiro, Matthew D, 1985. " An Unbiased Reexamination of Stock Market Volatility," Journal of Finance, American Finance Association, vol. 40(3), pages 677-87, July.
  9. Robert J. Shiller, 1980. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," NBER Working Papers 0456, National Bureau of Economic Research, Inc.
  10. Gilles, Christian & LeRoy, Stephen F, 1991. "Econometric Aspects of the Variance-Bounds Tests: A Survey," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 753-91.
  11. Flavin, Marjorie A, 1983. "Excess Volatility in the Financial Markets: A Reassessment of the Empirical Evidence," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 929-56, December.
  12. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-54, November.
  13. Charles Engel & Kenneth D. West, 2004. "Accounting for Exchange-Rate Variability in Present-Value Models When the Discount Factor Is Near 1," American Economic Review, American Economic Association, vol. 94(2), pages 119-125, May.
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